играть не последнюю роль(вариант требует замены конструкции: The team's success is due in no small part to the hard work of its players = Самоотверженные усилия членов команды играют не последнюю роль в ее успехе.merriam-webster.comAlexander Demidov)
не в последнюю очередь благодаря(to a great degree : largely or mostly
: The team's success is due in no small part to the hard work of its players.Artemie)
в значительной степени(to a great degree, largely or mostly: The team's success is due in no small part to the hard work of its players. MWALD Alexander Demidov)
в значительной степени благодаря(Tula has existed since at least 1146, when it was first mentioned on record. It grew into a metals and weapons manufacturing center under Peter the Great, thanks in no small part to native son Nikita Demidov, a blacksmith born in 1656 who founded the Demidov industrial dynasty. TMT Alexander Demidov)